Results 11 to 20 of about 269 (35)

COUNTING $S_5$ -FIELDS WITH A POWER SAVING ERROR TERM

Forum of Mathematics, Sigma, 2014
We show how the Selberg $\Lambda ^2$ -sieve can be used to obtain power saving error terms in a wide class of counting problems which are tackled using the ...
ARUL SHANKAR, JACOB TSIMERMAN
doaj   +1 more source

Differential resolvents of minimal order and weight

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 54, Page 2867-2893, 2004., 2004
We will determine the number of powers of α that appear with nonzero coefficient in an α‐power linear differential resolvent of smallest possible order of a univariate polynomial P(t) whose coefficients lie in an ordinary differential field and whose distinct roots are differentially independent over constants.
John Michael Nahay
wiley   +1 more source

Powersum formula for polynomials whose distinct roots are differentially independent over constants

International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 12, Page 721-738, 2002., 2002
We prove that the author′s powersum formula yields a nonzero expression for a particular linear ordinary differential equation, called a resolvent, associated with a univariate polynomial whose coefficients lie in a differential field of characteristic zero provided the distinct roots of the polynomial are differentially independent over constants.
John Michael Nahay
wiley   +1 more source

Multivariable dimension polynomials and new invariants of differential field extensions

International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 4, Page 201-214, 2001., 2001
We introduce a special type of reduction in the ring of differential polynomials and develop the appropriate technique of characteristic sets that allows to generalize the classical Kolchin′s theorem on differential dimension polynomial and find new differential birational invariants of a finitely generated differential field extension.
Alexander B. Levin
wiley   +1 more source

Divergence-free polynomial derivations [PDF]

, 2017
In this paper we present some new and old properties of divergences and divergence-free ...
Nowicki, Andrzej
core   +1 more source

On the canonical connection for smooth envelopes

, 2013
A notion known as smooth envelope, or superposition closure, appears naturally in several approaches to generalized smooth manifolds which were proposed in the last decades. Such an operation is indispensable in order to perform differential calculus.
Moreno, Giovanni
core   +2 more sources

A Note About the Nowicki Conjecture on Weitzenböck Derivations [PDF]

, 2009
2000 Mathematics Subject Classification: 13N15, 13A50, 16W25.We reduce the Nowicki conjecture on Weitzenböck derivations of polynomial algebras to a well known problem of classical invariant ...
Bedratyuk, Leonid
core  

Amitsur's theorem, semicentral idempotents, and additively idempotent semirings

Open Mathematics
The article explores research findings akin to Amitsur’s theorem, asserting that any derivation within a matrix ring can be expressed as the sum of an inner derivation and a hereditary derivation.
Rachev Martin, Trendafilov Ivan
doaj   +1 more source

Hasse--Schmidt derivations versus classical derivations

, 2020
In this paper we survey the notion and basic results on multivariate Hasse--Schmidt derivations over arbitrary commutative algebras and we associate to such an object a family of classical derivations. We study the behavior of these derivations under the
Narváez-Macarro, L.
core   +1 more source

Weitzenböck Derivations and Classical Invariant Theory II: The Symbolic Method [PDF]

, 2011
2000 Mathematics Subject Classification: 13N15, 13A50, 13F20.An analogue of the symbolic method of classical invariant theory for a representation and manipulation of the elements of the kernel of Weitzenböck derivations is ...
Bedratyuk, Leonid
core